Question

图形 $ABCD$ 是一个正方形。在这个正方形内画了三个较小的正方形，其边长如图所示。阴影的 L 形区域面积是

Figure $ABCD$ is a square. Inside this square three smaller squares are drawn with side lengths as labeled. The area of the shaded L-shaped region is

$7$

$10$

$12.5$

$14$

$15$

把阴影 L 形分成矩形。

Break the shaded L into rectangles

也可以用一个 $4\times4$ 正方形减去一个 $3\times3$ 正方形。

A $4\times4$ square minus a $3\times3$ square also works

可以从大正方形中减去上方的单位正方形、右下角的单位正方形，以及右上方的 $4 \times 4$ 正方形。

$ABCD$ 的阴影面积为 $5^2 - 2 \cdot 1^2 - 4^2 = 7\text{。}$

所以正确答案是 A。

We can subtract out the areas of the top unit square, the bottom right unit square, and the top right $4 \times 4$ square.

The shaded area in $ABCD$ is therefore $5^2 - 2 \cdot 1^2 - 4^2 = 7.$

Thus, A is the correct answer.